## dydlf 3 years ago PLEASE HELP MEEE :( consider the points P (-3, 0), Q (a, b) R (3, -3) and S (b+2,a+5). find the coordinates of Q and S if figure PQRS forms a parallelogram. okay so what i did is equate the slope and distances of lines PQ and RS... but i'm still not getting a final answer :(

1. dydlf

slope pq= slope rs--> b/(a+3)=(a+8)/(b-1) distance pq = distance rs --> (a+3)^2+b^2=(b-1)^2+(a+8)^2 so b=5a+28 tried to do systems but then there's no answer?!?!?! based on http://www.wolframalpha.com/input/?i=%28a%2B3%29%5E2%2Bb%5E2%3D%28b-1%29%5E2%2B%28a%2B8%29%5E2%3B+b%2F%28a%2B3%29%3D%28a%2B8%29%2F%28b-1%29 huhuhu someone help please :((

2. ghass1978

did you try solving it with vectors?

3. amistre64

im thinking of midpoints :)

4. amistre64

(P+R)/2 = (Q+S)/2 P+R = Q+S

5. amistre64

but that just gets me parallel lines that have no solution :/ a+b = -2 a+b = -8

6. amistre64

is there a figure to pull information off of?

7. amistre64

|dw:1345725961534:dw| we need to develop a notion of the rule that defines Q and S to narrow down the options eh

8. dydlf

what did you mean by your last message, amistre64? btw, is there anything wrong with my solution?

9. amistre64

a parallelagram is defined as opposite sides are parallel; i was just looking for "orbits" that would define the possibilities of 2 other points.

10. dydlf

ghass1978, nope i don't remember how to use vectors... it's not part of our exam. sorry

11. amistre64

your initial ideas look good in that they are defining valid properties

12. amistre64

is there a diagram that goes with this? or is it just a wordy problem?

13. dydlf

just that, exactly that :( waaaaahhh :(

14. dydlf

but it says PQRS which means the sequence of the coordinates would be that way. as in Q "between" P and R... if that's what you're wondering

15. amistre64

|dw:1345726700410:dw| without using the relationship between Q and S, we can get any number of values for Q and S

16. amistre64

Q(0,0) S(2,5) if we adjust this so that the midpoint is at 0,-1.5 it satisfies the rule Q(-1,-4) S(1,1) is a solution

17. dydlf

wait wait i don't get your drawing??? how did you get those? :( sorry!! i don't think we were taught that method yet?

18. dydlf

why get the midpoint?

19. amistre64

draw a parallelgram|dw:1345727410942:dw|

20. amistre64

|dw:1345727435579:dw||dw:1345727448036:dw|

21. amistre64

the midpoint of PR is the midpoint of QS , define some points that match the rule Q(a,b) S(b+2,a+5) and resolve the midpoint by moving the points about

22. amistre64

any scaled values of Q and S also work if there is a given picture to conform to, we can narrow down the odds of what they want tho

23. amistre64

|dw:1345727657560:dw|

24. SWAG

Nice work @amistre64

25. amistre64

thnx :)

26. dydlf

the right answer is S(5, -4) and Q(-9,3) ?? just found out now... how do you get that then? btw i will close this, have another question to ask.

27. amistre64

-9, 3 5,-4 ------ -4,-1 ; midpoint = -2,-1/2 -3, 0 3, -3 ------ 0,-3 ; midpoint = 0, -3/2 you either have some misinformation in the post, or the answer is wrong.

28. dydlf

okay wait so i did the midpoint thing but i'm still lost... midpoint of pr is (0, -3/2) midpoint of qs is ([a+b+2]/2, [a+b+5]/2) i tried equating [a+b+2]/2=0 and [a+b+5]/2=-3/2 then i got... a+b=-2 a+b=-8 ??? so how did you get Q(-1,-4) S(1,1) ?

29. dydlf

nevermind, i believe our teacher gave the wrong given. i believe s should have been (a+2, b+5)

30. amistre64

I essentially created a set of points in a different place that matched the given rule. Then I moved those points into the proper position.

31. amistre64

using your new rule for Q and S .... Q(a,b) S(a+2, b+5) select any values you want for a and b; say a=6 and b=-1 .... random picks Q(6,-1) S(6+2, -1+5) Q(6,-1) S(8, 4) now that I have a set of points that matches the rule, lets determine its own midpoint as is (7 , 3/2) now i want this midpoint to be at (0,-3/2), so lets see how we adjust it to get there (7 , 3/2) -7, -6/2 <---- i need to move Q and S by the same -------- (0, -3/2) since we have to move the midpoint by (-7,-3), we will have to move Q and S by the same amount Q(6,-1) S(8, 4) -7 -3 -7 -3 ------- -------- Q(-1,-4) S(1, 1) now we have a set of points Q and S that match the given rule; and is located in the proper spot